Which xiangqi endgames should I learn first?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws for movement, checkmate and both repetition rulings: a side that forces a repetition by perpetual check or perpetual chase loses rather than drawing. The chase half has not been validated against the official casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it before publishing.
Direct answer
Learn them in four layers. First the basic checkmates against a bare general, starting with chariots. Second, soldier endings, because a crossed soldier decides a huge number of real games. Third, the key defensive benchmarks, above all that a lone chariot against a full set of advisors and elephants is generally a draw with correct defence. Fourth, the minor-piece endings such as horse against cannon.
Layer one: the basic mates
These are the fundamental positions every stronger player can play without thinking: two chariots, chariot alone with your general's help, chariot with horse or cannon, horse with cannon, cannon with an advisor as its screen. Each teaches one idea about taking away the general's points. The basic checkmates page lays them out, and the reason some material is not enough is covered in the minimum material to win.
Layer two: soldiers
Most games that reach an endgame still have soldiers on the board, and a single crossed soldier is often the difference between a win and a draw. Learn how a soldier supports mates, why its height on the board matters, and how to stop one. The soldier endgames page is the place to start.
Layer three: what draws
Knowing which positions cannot be won saves you from trading into them when you are ahead, and tells you what to aim for when you are behind. The chariot against a full defence is the most important example, because it explains why players are careful about trading their last attacking pieces. See whether a chariot can beat advisors and elephants.
Layer four: minor pieces
Horse against cannon, horse or cannon with soldiers against defenders, chariot against a minor piece: these take longer to master, and they matter most once you are playing opponents who reach endgames with you regularly. Learn the first three layers well before going deep here.
Related questions
How do I practise them?
Set up a position on the analysis board and play it out until you can win, or hold, without hesitating. Then do it again from a slightly different start.
Should I study composed endgame problems too?
They are enjoyable and sharpen calculation, but the practical endings above win more games.